his report is my recent analysis of the EH antenna using the Pspice
program and considering the antenna as a set of circuit elements. The antenna can be
considered as a set of circuit elements because it is electrically small-meaning that the
phase delay that occurs as a wave travels the maximum length of the antenna is a small
fraction of an RF cycle. This means that all voltages and currents set up in the circuit
can be considered the same anywhere on a particular wire in the antenna that one might
test with a voltmeter or ammeter. If it were electrically large, one would need a Smith
Chart to calculate the voltages and currents on its wires.

The analysis below generates and uses many curves.These
curves are full of data, but the real INFORMATION is contained in the changes in the
curves as some parameter in the antenna is changed.I
often use a sort of "differential analysis" where I hold everything in a system
constant except one parameter, which I then tweak about while watching the system
response. This is a natural way of learning about somethingjust watch how a 2 year
old approaches a mysterious new object in his/her world: the object is tweaked, wiggled,
tasted, etc., until its properties are understood.So,
I recommend the reader sort of defocus, stand back a bit and try to watch the movement of
the curves as circuit element properties are changed.The
EH's basic component, the Isotron, is simply a large inductor and small capacitor with a
long physical spacing between plates wired as a series-tuned circuit. Energy stored in the
inductor as 1/2*inductance*(current)squaredis
stored in the capacitor as 1/2*capacitance*(voltage)squared a quarter of an RF cycle
later.The voltage is very high, which is why these
devices might be called "Tesla coil antennas".

EH DEFINED
Essentially, the EH antenna consists of two "Isotron" style antennas in parallel
across the transmission line. The radiation comes from the capacitors, which are in the
form of two cylinders separated by the cylinder diameter and pasted on a 4inch PVC pipe (click for metrics conversion). The length of
each cylinder is 1.5 x pipe diameter. The spacing between the cylinders is equal to the
pipe diameter. The coils are wound near each other below the cylinders on the pipe. The
tuning capacitor for 40 meters (7.0 MHz) is given as 63 pF. This information was taken
from Ted Hart's "almost book" about the EH antenna.

This analysis starts with the characteristics of a single
Isotron-type series tuned circuit. It then shows how the characteristics change when the
second Isotron circuit is added. Finally, the effect of capacitive coupling and resistance
between the radiating capacitors is shown. It is then noted that the coils are near each
other with a common axis, so they must inductively couple. The independent coils of the
first part of the analysis are exchanged for a transformer of the same inductance and
variable coupling and the analysis repeated. The coupled coil configuration is the same as
the "DLA" antenna that has been written up previously-the variable coupling
curves are similar to the DLA data and it is hoped that the changes in the series of
tuning curves versus coupling throws some light on the DLA operation.

This modeling shows that increasing the mutual coupling between the two Isotrons
changes the tuning by making the lower frequency Isotron tuning drop in frequency and
lower in Q while the upper frequency Isotron tuning rises in frequency and the Q
increases. This makes sense since mutual coupling increases the voltage in the one and
decreases the voltage in the other, as the Isotrons and coils are connected in opposite
directions across the cable. Very small values of coupling cause large changes in the
behavior of the combined Isotron system.

The analysis also shows there are three regions of importance for the phase of the
voltage between the radiating capacitors. The frequency range below and above both
resonant frequencies shows 180 degrees between ends . The frequency range between the
resonant frequencies shows a phase of zero degrees between ends of the antenna. The phase
shifts rapidly between the two values at the circuit resonance (not the combined
resonance, which moves around. The voltage on the end connected to the higher frequency
Isotron is in phase with the drive in all regions. This rapid change at the resonant
frequency and constant value at all other frequencies was a surprise to me, as I had been
expecting the gradual phase change seen in the single Isotron.

The Isotron itself is a series-tuned circuit and is a low impedance load on the cable,
near resonance. Two isotrons in parallel are a high impedance in the frequency region
between individual resonant frequencies. In that frequency region, one Isotron is
operating above its resonant frequency and is inductive. The other Isotron is operating
below its resonant frequency, and appears capacitive. The net result is a parallel tuned
circuit of an inductor and a capacitor-a high impedance load to the cable.

Since the EH antenna is electrically small, there cannot be any directivity due to the
effects of aperture. The point source may vary in power in different directions because of
variation in the projected E and H fields in a plane perpendicular to the direction. In
the EH antenna, the E fields are either from end to end, or both ends in phase to ground.
Small spacing changes between the end cylinders may adjust the capacitance, capacitive
coupling, and the resultant tuning caused by the coupling between isotrons, but the
changes will not vary the directivity.

A SINGLE ISOTRON
The Figure 1 group shows a single series-tuned circuit or "Isotron". The circuit
is in Figure 1a: L1 and C1 are the Isotron. Point 3 is the cable and R1 is the cable
impedance of 50 ohms. Ignore the other circuit elements in the Figure 1 groupthey
are all grounded groups of elements such as the other Isotron and the coupling between the
two antennas. It was easier to place the elements in the schematic and ground them for
experiments that didn't use them than to redraw the schematic each time a condition
changed.

Figure 1b shows the essential characteristics of the Isotron series-tuned circuit. The
lower part of the Figure shows the various voltages in the circuit vs frequency. The cable
voltage (V3) shows a low-impedance load at resonance at 7 MHz. The capacitor voltage (V4)
shows a peak at this frequency. The other Isotron capacitor is grounded and its voltage,
(V5) or V(L2:2) is zero. The upper part of figure 1b shows the phase of the radiating
capacitor voltage V4. At resonance, the phase is -90 degrees.

Figure 1c: Shows where input impedance
= 50 ohms (v(3)=0.5

Figure 1c changes the scale of the voltage plots to 1 volt full scale from the value of
24.93 volts in figure 1b. This clearly shows the loaded cable voltage, (V3) and the null
at resonance. The cable is closest to being matched when the voltage V3 == 0.5 volts.
There, the load resistance is equal to the source resistance of 50 ohms. The cursor table
in the figure shows that the voltage A1 is 0.502 volts at 6.832 MHz. The vertical finely
dotted line is the A1 cursor. The sparsely dotted line is the A2 cursor. It is showing
V(l2:2) or V5, the capacitor voltage on the other grounded Isotron that equals zero. This
cursor is set at 6.9 MHz. The Isotron has two possible matched points, above and below
resonance, where V3 (the blue line) crosses 0.5 volts. The dotted cursor lines surround
their associated colored identifier symbols across the bottom of the figure.

ADD A SECOND ISOTRON
Figure 2a shows the schematic for the two isotrons in parallel. L1 -C1 is the lower
frequency Isotron. L2-C2 is the higher frequency Isotron. The coupling between the two is
still grounded and out of play.

Figure 2a: Two Isotrons wired to make
an EH antennaOne tuned high, one tuned low

Figure 2b: The two Isotrons combine to
load the cable withtwo tuned circuits symmetrically about the center frequency

Figure 2b shows the voltage plots. The cable voltage V3 is green and it shows the
expected two nulls at the resonant frequency of the two isotrons. The capacitor voltages
are red and blue and show a peak between the center frequency of the system of two
Isotrons and the respective individual resonant frequencies. Note that the phase between
the voltage at the antenna ends is quite different from that in Figure 1. It abruptly
changes from -180 degrees above and below the two resonant frequencies of the system to
-360 degrees == zero degrees between the two nulls in V3. No more gradual change in phase
with frequency! This change happens at the real resonant frequencies of each Isotron. Note
also the perfect symmetry about the center frequency of the system. The yellow curve shows
the voltage difference between the ends of the antenna. At the center frequency of the
system, the voltage at the two ends is in phase and is equal-the difference is zero
(strictly speaking, the difference == the drive voltage V3).

Figure 2c: At center frequency the
combination is a high impedance-- a parallel-tuned circuit (green = cable load)

Figure 2c is the voltage plot showing the bottom 3.74-volt range. Note the two nulls in
the cable load voltage V3. The cursor is at the center frequency of the system. Now, note
the voltage at the cable: 0.996 volts from a 1-volt source! This is a high impedance
pointthe current is 80 uA and the load is 12.5k ohms to drop the voltage
only .004 volts coming from a 50-ohm source! Each Isotron tuning null is a
zero drive point for the other Isotron as well as a maximum voltage point for its own
capacitor, since the two Isotrons are in connected parallel across the cable.

ADD ONLY 10 pF END TO END COUPLING
The Figure 3 group show what just 10 pF coupling between the two cylinders does. Figure 3a
shows the circuit. The coupling is C3 and there is a megohm of resistance to simulate a
small amount of radiation in place. V4 and V5 are the two capacitor or cylinder voltages
for the two Isotrons.

Figure 3b: The phase between the ends
remains atzero degrees near the center frequency

Figure 3b shows that the low frequency resonance has moved off the screen to the left.
The high frequency Isotron resonance is much narrower in bandwidth and has moved a small
amount to the left. Note that the phase changes in V4-V5 (the cylinder to cylinder
voltage) are only slightly moved in position. They still are near the real
resonance of each Isotron!!

Figure 3c: The combination is no
longer matched -- Coupling hurts!

Figure 3c is a magnified version of the frequency region around the higher frequency
Isotron. Note the whole screen is only 400 kHz wide. The cursor shows that loaded cable
voltage is 0.9981 volts-down 38 uV from the source voltage. The load is 26k ohms. A little
coupling changes things drastically.

LOWER THE RESISTOR REPRESENTING RADIATION LOAD TO 2k
The Figure 4 group show what might happen if the system were to have a radiation
resistance of 2000 ohms. This is where the load would be if the voltage from cylinder to
cylinder were out of phase. But, the voltages on the cylinders are in phase; so all fields
are outward from the two cylinders to the cable ground. The load on the cable is still a
high impedance load.

Figure 4a: A low radiation resistance
loads the circuit,destroys the symmetry, but does not help the matching

Figure 4b: The loading drops the
voltage on both ends at once

Figure 4a shows the circuit. Figure 4b shows the tuning curves. The effect of the 2k
resistor is to load down the lower frequency Isotron and to smooth out the phase change at
the real resonant frequency of this component. Note that the phase change related to the
upper frequency Isotron is still near the real resonant frequency. Also, note that the
maximum capacitor voltage is less than half of what it was without the 2k load that was
represented in the Figure 3 group.

The two inductors are wound on the pipe below the cylinders, along the axis of the
pipe. They must have some inductive coupling. All of the curves discussed so far are for
the condition where the coils are independent and not coupled. The next series of curves
show what happens when there is inductive coupling between the inductors.

REPRESENT THE COILS WITH A TRANSFORMER
WITH THE SAME INDUCTANCE AS L1 AND L2
Figure 5a shows the circuit with only inductive coupling. The coupling transfers some of
the energy from one Isotron to the other.

Figure 5a: Inductive coupling between
the coils (=K) is inherent in the structure

The Figure 5b group is a series of frequency scans at different coupling coefficients,
k, from 0.001 to 0.2. The lowest coupling gives curves that look like Figure 2-symmetrical
about the center frequency of the system. As k increases, two things happen. First, the
lower frequency Isotron moves lower in frequency and the width of the pattern increases.
The Q of this Isotron is lowered. The higher frequency Isotron moves upward in frequency
and its pattern narrows. Its Q increases. Second, the abrupt phase shifts between the
cylinders accompany the pattern of the higher frequency Isotron in its movement. At higher
k values, the cylinder voltages are out of phase (180 degrees) over the whole pattern of
the lower frequency Isotron.

Figure 5b: Increasing coupling spreads
the resonances apart,
lowers the Q of one and raises the Q of the otherClick for Figure 5b Group

Figure 5c shows the lowest 1-volt range of the figure 5b curves. The loaded cable
voltage crosses the 0.5-volt value twice for each Isotron, except at the highest coupling,
where the upper frequency Isotron just gets down to 50 ohms at the bottom of its null. For
k > 0.2, it would never be a matched load. The inductive coupling between Isotrons
gives 3 or 4 chances to be matched, with different voltages between the cylinders or from
the cylinders to ground.

I should observe here that I first found this strange double resonance with a DLA that
had a k of 0.82 and no radiating capacitors-just radiating coils. The spacing between high
and low resonant frequencies was enough that I tried to make a dual band 40- and 20-meter
version! I didn't recognize the coupling association until this study.

ADD THE CAPACITIVE COUPLING BETWEEN THE CYLINDERS
Figure 6a shows the capacitive coupling between Isotrons. Figure 7a is the same except the
coupling is increased to 20pF. The inductive coupling was set at 0.02 for these curves.

Figure 6a & 7a: Coupling between
the ends does the same kind of thing

The Figure 6b group shows the patterns for three values of coupling capacitor: 1pF, 4pF
and 10 pF. The highest value has about the same amount of effect as the inductive k of
0.2, and all the effects are the same for either kind of coupling.

Figure 6b: The tuning spreads but the
phasebetween ends is still zero or 180 degrees

Figure 6c: A wider scan shows where
the lower resonance went

Figure 6c shows the bottom 1-volt range for the two lowest couplings. Note that just
4pF coupling is enough to raise the impedance at the highest resonant frequency to a value
greater than 50 ohms, while the resonant pattern has the usual two matched frequencies.
For the 10pF coupling, the frequency scan was widened to completely show the lower
frequency pattern. Figure 6d shows the bottom 1 volt of the patterns. The yellow line in
figure 6d shows the 0.5-volt level where the cable voltage V3 is matched.

Figure 6d: There are still only two
matched points
It looks like only one isotron!

INCREASE THE CAPACITIVE COUPLING TO 20 pF
Figure 7b shows the effect of 20pF and k=0.02. The lower frequency resonant point is moved
from around 7 MHz to about 4.6 MHz while the higher resonant point is under 8 MHz. Figure
7c shows the bottom 1-volt range to help locate the matched points.

Figures 8a and 8b show that increasing the k ten times, to 0.2, only moves the lower
frequency resonant point from 4.6 to about 4.3 MHz. Both types of coupling work together
in the same directions.

Figure 8a: 10x inductor coupling
doesn't changethings too much with high end coupling

Figure 8b: Still matched only at lower
frequency -- it looks like only 1 isotron!

MY CONCLUSIONS
The EH antenna appears to be simply two Isotrons combined to give the effect of a single,
much lower frequency Isotron. As such, I would expect it to radiate numbers that seem to
average about an S unit (-20 db) down from a dipole.

The EH antenna is a member of the class of antennas where coupling between two
radiating tuned circuits, a factor poorly controlled in most designs, can produce great
tuning changes. This factor works against any possible meaningful merits worth comparing
the other various EH constructions.

The abrupt phase transitions and broad regions of unchanging phase over many different
tuning and coupling conditions suggest that trying to tweak the phase to produce CFA-like
conditions is doomed to failure. I think any variations in
performance observed are due more to the movement of the resonance patterns in frequency
than to any field interactions. -30-

Worked for 16 years designing electronic
countermeasures against monopulse and pulse compression radars, including remote means of
bending the radar's antenna pattern, and have designed and built an instrumentation radar.

Worked for about 15 years as an electronic consultant designing and troubleshooting
microwave anechoic chambers using chamber simulation computer programs I wrote for the
purpose. Designed and built (I have a machine shop) test fixtures to measure the
electronic properties of materials and absorbers. Have written computer programs to do
stock market analysis and to encrypt documents using simulated rotor machine coders.

Was first licensed as W9TPH in 1952, then K1ZLJ but let it lapse in the 1960's. Retested
and passed General class this summer, and Extra class this fall. After relocating from the
East Coast to the West Coast in Oregon, USA, now, having put the ocean on the left instead
of the right. Am interested in compact antennas to fit in my postage stamp of land looking
out over the pacific ocean.